I am making a website for a side project at school where students enter the classes they need to take, what days they want or don't want classes, and when they cant have or don't want classes. The basics are there are classes, and each class has many sections at different times with different professors that a student can choose from. With the freshman level classes, there can be over 30 different sections for each class. I have the classes and sections in a mysql database and I have been coding in php.
So far I have it working but I want to make it faster. I have been reading about other scheduling problems but I am looking for specifics to what I am doing. This isn't making schedules from scratch. It is making schedules from what sections are available and ranking them based on what the students inputs. Currently for few possible sections, it runs fast. But when the possible schedules get to about 300,000, it takes around 30 seconds to compare and rank everything. I have been improving it by changing how schedules are generated but I want to faster. I switched from brute force generating to using a tree based method.
I'm not asking for homework help or for someone to do this for me. I just want to be pointed in the right direction with already existing problems and algorithms that I can learn about.